Related papers: BMS algebras in 4 and 3 dimensions, their quantum …
Twisted deformations of the conformal symmetry in the Hopf algebraic framework are constructed. The first one is obtained by a Jordanian twist built up from dilatation and momenta generators. The second is the light-like…
We construct the full quantum algebra, the corresponding Poisson-Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS)…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
We study the symmetries of the N=1 exactly marginal deformations of N=4 Super Yang-Mills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup.…
The dissertation presents possibilities of applying noncommutative spacetimes description, particularly kappa-deformed Minkowski spacetime and Drinfeld's deformation theory, as a mathematical formalism for Doubly Special Relativity theories…
Twists of four-dimensional supersymmetric quantum field theories (SQFTs) isolate protected sectors with rich algebraic structures. We develop a unified framework for analyzing symmetries and anomalies in four-dimensional holomorphically…
We analyze the residual gauge freedom in gravity, in four dimensions, in the light-cone gauge, in a formulation where unphysical fields are integrated out. By checking the invariance of the light-cone Hamiltonian, we obtain a set of…
We propose a solution to a classic problem in gravitational physics consisting of defining the spin associated with asymptotically-flat spacetimes. We advocate that the correct asymptotic symmetry algebra to approach this problem is the…
Asymptotic symmetries of electric and magnetic Carrollian gravitational theories with a negative cosmological constant $\Lambda$ are analyzed in 3+1 space-time dimensions. In the magnetic theory, the asymptotic symmetry algebra is given by…
We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…
The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…
Recently symmetries of gravity and gauge fields in the asymptotic regions of spacetime have been shown to play vital role in their low energy scattering phenomena. Further, for the black hole spacetime, near horizon symmetry has been…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
BMS algebra in three spacetime dimensions can be deformed into a two parameter family of algebra known as $W(a,b)$ algebra. For $a=0$, we show that other than $W(0,-1)$, no other $W(0,b)$ algebra admits a non-degenerate bilinear and thus…
The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. As in the Bondi-Metzner-Sachs gauge, it is shown to be isomorphic to the direct sum of the abelian…
Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between…
A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf…
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat spacetime. It is infinite dimensional and entails an infinite number of conservation laws. According to the black hole membrane…
These notes are an introduction to asymptotic symmetries in gauge theories, with a focus on general relativity in four dimensions. We explain how to impose consistent sets of boundary conditions in the gauge fixing approach and how to…
We study the finite distance boundary symmetry current algebra of the most general first order theory of 3d gravity. We show that the space of quadratic generators contains diffeomorphisms but also a notion of dual diffeomorphisms, which…